ky2+(k+1)y+k-1=0

Apply the distributive property.

ky2+ky+1y+k-1=0

Multiply y by 1.

ky2+ky+y+k-1=0

ky2+ky+y+k-1=0

Subtract y from both sides of the equation.

ky2+ky+k-1=-y

Add 1 to both sides of the equation.

ky2+ky+k=-y+1

ky2+ky+k=-y+1

Factor k out of ky2.

k(y2)+ky+k=-y+1

Factor k out of ky.

k(y2)+k(y)+k=-y+1

Raise k to the power of 1.

k(y2)+k(y)+k=-y+1

Factor k out of k1.

k(y2)+k(y)+k⋅1=-y+1

Factor k out of k(y2)+k(y).

k(y2+y)+k⋅1=-y+1

Factor k out of k(y2+y)+k⋅1.

k(y2+y+1)=-y+1

k(y2+y+1)=-y+1

Divide each term in k(y2+y+1)=-y+1 by y2+y+1.

k(y2+y+1)y2+y+1=-yy2+y+1+1y2+y+1

Cancel the common factor of y2+y+1.

Cancel the common factor.

k(y2+y+1)y2+y+1=-yy2+y+1+1y2+y+1

Divide k by 1.

k=-yy2+y+1+1y2+y+1

k=-yy2+y+1+1y2+y+1

Simplify -yy2+y+1+1y2+y+1.

Move the negative in front of the fraction.

k=-yy2+y+1+1y2+y+1

Combine the numerators over the common denominator.

k=-y+1y2+y+1

Factor -1 out of -y.

k=-(y)+1y2+y+1

Rewrite 1 as -1(-1).

k=-(y)-1(-1)y2+y+1

Factor -1 out of -(y)-1(-1).

k=-(y-1)y2+y+1

Simplify the expression.

Rewrite -(y-1) as -1(y-1).

k=-1(y-1)y2+y+1

Move the negative in front of the fraction.

k=-y-1y2+y+1

k=-y-1y2+y+1

k=-y-1y2+y+1

k=-y-1y2+y+1

Solve for k ky^2+(k+1)y+k-1=0